y = f(ax) is a stretch in the x direction, the scale factor is 1/a
x coordinate: divide by a
y coordinate: no change
y = af(x) is a stretch in the y direction, the scale factor is a
x coordinate: no change
y coordinate: multiply by a
y = f(-x) is a reflection in the y axis
x coordinate: change sign
y coordinate: no change
y = -f(x) is a reflection in the x axis
x coordinate: no change
y coordinate: change sign
with transformations except reflections, if the change is outside the bracket it affects the y coordinate in the way you would expect, and if the change is inside the bracket it affects the x coordinate in the opposite way to what you would expect
y = (ax + b) is a translation by -b then a stretch by 1/a, you need to do it in this order not the reverse to get the correct graph